How to find the area of a rectangle

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ISEE Middle Level Quantitative Reasoning › How to find the area of a rectangle

1 - 10

What is the area of the figure below?

CORRECT

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

3.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=11\times 3$ $A=3\times 3$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

6.5

CORRECT

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

6.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=5\times 10$ $A=5\times 3$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

CORRECT

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 3$ $A=6\times 3$

To find our final answer, we need to add the areas together.

What is the area of the figure below?

CORRECT

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=8\times 4$ $A=7\times 4$

To find our final answer, we need to add the areas together.

Find the area of a rectangle with a length of 14in and a width that is half the length.

$98\text{in}^2$

CORRECT

$42\text{in}^2$

$21\text{in}^2$

$7\text{in}^2$

$72\text{in}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 14in. We also know the width of the rectangle is half the length. Therefore, the width is 7in.

Knowing this, we will substitute into the formula. We get

$\text{area of rectangle} = 14\text{in} \cdot 7\text{in}$

$\text{area of rectangle} = 98\text{in}^2$

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

CORRECT

Explanation

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

To find the area of a rectangle, we must perform the following:

$A_{Rectangle}=l*w$

Where l and w are our length and width.

This means we need to multiply the given measurements. Be sure to use the right units!

And we have our answer. It must be centimeters squared, because we are dealing with area.

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

CORRECT

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

CORRECT

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .